diff --git a/crates/engine/src/canvas/shape_handles.rs b/crates/engine/src/canvas/shape_handles.rs
index 726f7d011..b286010ba 100644
--- a/crates/engine/src/canvas/shape_handles.rs
+++ b/crates/engine/src/canvas/shape_handles.rs
@@ -139,6 +139,11 @@ fn count_at(n: &Node, q: Point) -> Option<f64> {
         return None;
     }
     let (x, y) = (q.x / rx - 1.0, q.y / ry - 1.0);
+    // On the centre there is no direction (atan2 of two zeros would read as 180 degrees): treat it
+    // as no angle, the most points.
+    if x.hypot(y) < 1e-9 {
+        return Some(COUNT_MAX);
+    }
     let angle = x.atan2(-y).rem_euclid(std::f64::consts::TAU).to_degrees();
     let count = (360.0 / angle.max(1e-9)).round();
     count.is_finite().then(|| count.clamp(COUNT_MIN, COUNT_MAX))
diff --git a/crates/engine/src/shape_handles_tests.rs b/crates/engine/src/shape_handles_tests.rs
index 65220d7a7..0e3a2f211 100644
--- a/crates/engine/src/shape_handles_tests.rs
+++ b/crates/engine/src/shape_handles_tests.rs
@@ -160,10 +160,10 @@ fn dragging_the_count_handle_sets_the_count_by_the_angle_about_the_centre() {
     // The readout is the count.
     let doc = s.doc().unwrap();
     assert_eq!(crate::shape_handles::value(doc, poly, ShapeHandle::Count), Some(4.0));
-    // The finite guard: a pointer on the centre gives a finite count.
+    // A pointer on the centre has no direction: it gives the most points.
     let h = count_handle(&s, poly);
     drag(&mut s, (h[0], h[1]), (100.0, 100.0), false);
-    assert!((3..=60).contains(&count_of(&s, poly)));
+    assert_eq!(count_of(&s, poly), 60, "a pointer on the centre");
 }
 
 #[test]